Exam
Name___________________________________

SHORT ANSWER.  Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
1) A local juice manufacturer distributes juice in bottles labeled 12 ounces. A government agency thinks that the company is cheating its customers. The agency selects 20 of these bottles, measures their contents, and obtains a sample mean of 11.7 ounces with a standard deviation of 0.7 ounce. Use a 0.01 significance level to test the agency's claim that the company is cheating its customers. Round the test statistic to the nearest thousandth.	1)  _____________

2) A bank claims that the mean waiting time in line is less than 2.2 minutes. A random sample of 20 customers has a mean of 2 minutes with a standard deviation of 0.8 minute. If  test the bank's claim using P-values.	2)  _____________

3) A local eat-in pizza restaurant wants to investigate the possibility of starting to deliver pizzas. The owner of the store has determined that home delivery will be successful if the average time spent on the deliveries does not exceed 40 minutes. The owner has randomly selected 22 customers and has delivered pizzas to their homes in order to test if the mean delivery time actually exceeds 40 minutes.  Suppose the P-value for the test was found to be 0.0281. State the correct conclusion.	3)  _____________

4) A local eat-in pizza restaurant wants to investigate the possibility of starting to deliver pizzas. The owner of the store has determined that home delivery will be successful if the average time spent on the deliveries does not exceed 30 minutes. The owner has randomly selected 17 customers and has delivered pizzas to their homes in order to test if the mean delivery time actually exceeds 30 minutes.  Suppose the P-value for the test was found to be 0.0295. State the correct conclusion.	4)  _____________

5) A local eat-in pizza restaurant wants to investigate the possibility of starting to deliver pizzas. The owner of the store has determined that home delivery will be successful if the average time spent on the deliveries does not exceed 28 minutes. The owner has randomly selected 24 customers and has delivered pizzas to their homes in order to test if the mean delivery time actually exceeds 28 minutes.  Suppose the P-value for the test was found to be 0.0281. State the correct conclusion.	5)  _____________

6) An airline claims that the no-show rate for passengers is less than 5%. In a sample of 420 randomly selected reservations, 19 were no-shows. At α = 0.01, test the airline's claim. Round  to the nearest thousandth when calculating the test statistic.	6)  _____________

7) A recent study claimed that at least 15% of junior high students are overweight. In a sample of 160 students, 18 were found to be overweight. At α = 0.05, test the claim.	7)  _____________

8) In one city, 25 out of 100 randomly sampled teenagers say that they smoke.
(a) Consider the hypotheses  p =  0.23 versus  p > 0.23. Explain what the researcher would be testing. Perform the test at the α = 0.05 level of significance. Write a conclusion for the test. Round the test statistic to the nearest hundredth.
(b) Repeat part (a) for the hypotheses  p = 0.24 versus  p > 0.24.
(c) Based on your results in parts (a) and (b), write a few sentences that explain the difference between "accepting" the statement in the null hypothesis versus "not rejecting" the statement in the null hypothesis.	8)  _____________

9) Fifty percent of registered voters in a congressional district are registered Democrats. The Republican candidate takes a poll to assess his chances in a two-candidate race. He polls 1200 potential voters and finds that 621 plan to vote for the Democratic candidate. Does the Republican candidate have a chance to win? Use α = 0.05.	9)  _____________

1) critical value  = -2.539; standardized test statistic ≈ -1.917; fail to reject ; There is not sufficient evidence to support the government agency's claim.
2) Standardized test statistic ≈ -1.118; Therefore, at 19 degrees of freedom, the P-value must lie between 0.10 and 0.25. Since the P-value > α, fail to reject . There is not sufficient evidence to support the bank's claim.
3) At α = 0.025, we fail to reject .
4) At α = 0.025, we fail to reject .
5) At α = 0.025, we fail to reject .
6) critical value  = -2.33; standardized test statistic ≈ -0.45; fail to reject ; There is not sufficient evidence to support the airline's claim.
7) critical value  = -1.645; standardized test statistic ≈ -1.33; fail to reject ; There is not sufficient evidence to reject the claim.
8) (a) The researcher would be testing whether more than 23% of teenagers in the city smoke.
n(1 - ) = 17.71 > 10
Critical value  = 1.645;  Test statistic z = 0.48
Do not reject the null hypothesis. There is not sufficient evidence at the α = 0.05 level of significance that more than 23% of teenagers in the city smoke. 

(b) The researcher would be testing whether more than  24% of teenagers in the city smoke. 
n(1 - ) = 18.24 > 10
Critical value  = 1.645;  Test statistic z = 0.23
Do not reject the null hypothesis. There is not sufficient evidence at the α = 0.05 level of significance that more than 24% of teenagers in the city smoke.

(c) "Accepting" the null hypothesis can lead to contradictory conclusions, whereas "not rejecting" it does not. If we accept the null hypothesis, then in part (a) we are "accepting" that the population proportion is equal to 0.23 and in part (b) we are "accepting" that the population proportion is equal to 0.24. This means that we have used the same data to conclude that the population proportion is equal to two different values. If we "fail to reject" the null hypothesis then , rather than concluding that the population proportion is equal to 0.23 (or 0.24) we are simply saying that these values cannot be ruled out. 
9) critical value  = 1.645; standardized test statistic ≈ 1.21; fail to reject ; There is not sufficient evidence to support the claim p > 0.5. The Republican candidate has no chance.